Starting with polynomial:
P : t^22 - 231*t^20 + 21945*t^18 - 1119195*t^16 + 33575850*t^14 - 611080470*t^12 + 6721885170*t^10 - 43212118950*t^8 + 151242416325*t^6 - 252070693875*t^4 + 151242416325*t^2 - 13749310575
Extension levels are: 22 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : t^22 - 231*t^20 + 21945*t^18 - 1119195*t^16 + 33575850*t^14 - 611080470*t^12 + 6721885170*t^10 - 43212118950*t^8 + 151242416325*t^6 - 252070693875*t^4 + 151242416325*t^2 - 13749310575
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 133192556749715850898883777857029/104779331696056756994688859075*t^57 + 157323832934608034350646554715242383/209558663392113513989377718150*t^55 - 264111886199418518480894574436934368587/963969851603722164351137503490*t^53 + 66830782682385618075431914842392027308911/963969851603722164351137503490*t^51 - 2494209711153774364606878857227170976738617/192793970320744432870227500698*t^49 + 891079500337080116739726319460390516924327643/481984925801861082175568751745*t^47 - 99963685163894018699863244238031808662894756893/481984925801861082175568751745*t^45 + 1790730784669334666851538905292453312286285830508/96396985160372216435113750349*t^43 - 129568887993398582661998524940391024661179283722456/96396985160372216435113750349*t^41 + 1174437386309121179569434644853411823687117587015975/14830305409288033297709807746*t^39 - 56633330300219498697244053146813430951415046528567769/14830305409288033297709807746*t^37 + 2241550270288475803770382435488331961355454418053547169/14830305409288033297709807746*t^35 - 72886253958062268754636093906957951141290364336743765555/14830305409288033297709807746*t^33 + 972645481132569009868964555011667837713087488092649601650/7415152704644016648854903873*t^31 - 21253255899743030066008766138875231197037577363765194425150/7415152704644016648854903873*t^29 + 378601358471919279486959819014505631805020352399020927122925/7415152704644016648854903873*t^27 - 5465096136462088702948066851697261721194748243128057819829475/7415152704644016648854903873*t^25 + 126825778927931783688695781570307444202263812034172581707487875/14830305409288033297709807746*t^23 - 50900314259127202795262127614992297993170947478053514107914875/644795887360349273813469902*t^21 + 368892058897060237176233710796037757693458204724678804789044375/644795887360349273813469902*t^19 - 2064232006794952016469249466129428640028999622463207992397711125/644795887360349273813469902*t^17 + 4365178114891828375976909398129475327882323198305898034429827125/322397943680174636906734951*t^15 - 13573226541764359512112877067644374622643025796184740306915821875/322397943680174636906734951*t^13 + 29911914200461134873040614993160480513368215763863574827281526250/322397943680174636906734951*t^11 - 44423813864699791233190060700988796981266212161860680373873731250/322397943680174636906734951*t^9 + 82690123261719371557722400654468672889829855720797022720678384375/644795887360349273813469902*t^7 - 43059770877605033865122550893866932647923414272348478771780115625/644795887360349273813469902*t^5 + 10260314917027782078966752663381082515573578632233123841373265625/644795887360349273813469902*t^3 - 704503478680034222476782987315170565972480441964681437177046875/644795887360349273813469902*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-11.077705621024702921 + 7.469593638581573125e-926j)  +/-  (1.24e-243, 1.24e-243j)
| (6.9859804240188138349 + 5.4670036203114897468e-925j)  +/-  (3.42e-241, 3.42e-241j)
| (6.0730749511228975445 - 4.0110333862701358346e-938j)  +/-  (8.7e-242, 8.7e-242j)
| (11.077705621024702921 - 3.9779920262671364811e-949j)  +/-  (1.24e-243, 1.24e-243j)
| (2.0068019604802216843 - 1.6641338758525073096e-953j)  +/-  (3.7e-248, 3.7e-248j)
| (12.780083554857161853 - 2.7320421077976728628e-950j)  +/-  (8.55e-246, 8.55e-246j)
| (-11.848834761312194371 + 3.2234589992483929998e-950j)  +/-  (1.5e-244, 1.5e-244j)
| (-9.7559812617478849822 - 1.198027969529319967e-947j)  +/-  (2.19e-242, 2.19e-242j)
| (8.6009702081088291466 + 3.5857992844746242238e-946j)  +/-  (1.5e-241, 1.5e-241j)
| (10.389753859947853791 - 9.7150865813260316151e-954j)  +/-  (6.23e-243, 6.23e-243j)
| (-12.780083554857161853 + 1.3967559553159565084e-965j)  +/-  (8.65e-246, 8.65e-246j)
| (4.8607747939465193904 - 9.2078781704915266063e-961j)  +/-  (8.56e-243, 8.56e-243j)
| (7.389945036208990253 + 5.5372218897870849469e-968j)  +/-  (8.28e-241, 8.28e-241j)
| (-5.6476791643015140686 - 1.3754089930348998248e-984j)  +/-  (4.11e-242, 4.11e-242j)
| (7.634842054526153498 + 3.2106541857298717643e-982j)  +/-  (8.13e-241, 8.13e-241j)
| (-0.99516242227121542187 - 6.0583228259224932444e-1002j)  +/-  (2.71e-251, 2.71e-251j)
| (1.3246623257943697578 - 3.1258935525580382414e-1001j)  +/-  (3.35e-250, 3.35e-250j)
| (-4.8607747939465193904 - 9.8516389365032781049e-993j)  +/-  (8.39e-243, 8.39e-243j)
| (-2.3417599962877077336 - 1.0482426632474853473e-997j)  +/-  (2.83e-247, 2.83e-247j)
| (5.6476791643015140686 + 2.2675276460013061595e-992j)  +/-  (4.43e-242, 4.43e-242j)
| (9.162078295726944468 + 1.7679836253427924687e-991j)  +/-  (5.9e-242, 5.9e-242j)
| (-3.0324042278316759091 - 2.9391846321121480724e-1001j)  +/-  (1.06e-245, 1.06e-245j)
| (-3.7414963502665176946 - 1.7945863005653285867e-999j)  +/-  (2.45e-244, 2.45e-244j)
| (8.0740299840217109612 - 5.0463012855094729502e-996j)  +/-  (3.7e-241, 3.7e-241j)
| (-8.0740299840217109612 + 1.1834013108372447283e-1000j)  +/-  (3.56e-241, 3.56e-241j)
| (-7.389945036208990253 + 4.4364012020213894352e-1000j)  +/-  (8.83e-241, 8.83e-241j)
| (11.848834761312194371 + 7.5490547256556566432e-1009j)  +/-  (1.47e-244, 1.47e-244j)
| (9.7559812617478849822 - 1.3614745755941642803e-1005j)  +/-  (2.23e-242, 2.23e-242j)
| (4.1005678299003455187 - 1.3066077416645341067e-1007j)  +/-  (9.3e-244, 9.3e-244j)
| (-10.389753859947853791 - 1.4159596297267493896e-1007j)  +/-  (6.13e-243, 6.13e-243j)
| (-6.9859804240188138349 + 2.2473391509648594372e-1005j)  +/-  (3.63e-241, 3.63e-241j)
| (3.7414963502665176946 - 4.9677911989114118548e-1011j)  +/-  (2.5e-244, 2.5e-244j)
| (2.6797095161691591287 - 1.4331520068961376698e-1013j)  +/-  (1.76e-246, 1.76e-246j)
| (-8.6009702081088291466 + 3.3038636974411024526e-1008j)  +/-  (1.61e-241, 1.61e-241j)
| (-9.162078295726944468 - 1.3776106378936366544e-1009j)  +/-  (6.18e-242, 6.18e-242j)
| (-6.5231474192115931067 + 1.0476166043337732882e-1012j)  +/-  (1.72e-241, 1.72e-241j)
| (6.5231474192115931067 + 1.5276541802520557742e-1016j)  +/-  (1.78e-241, 1.78e-241j)
| (1.6641248391179069719 - 8.024158175825529829e-1037j)  +/-  (4e-249, 4e-249j)
| (-4.4763619773108684158 + 2.0808274688560476193e-1028j)  +/-  (2.87e-243, 2.87e-243j)
| (-6.0730749511228975445 - 9.7524106022840736481e-1028j)  +/-  (9e-242, 9e-242j)
| (-7.634842054526153498 + 7.5781004206648224812e-1030j)  +/-  (8.69e-241, 8.69e-241j)
| (-0.66509007143132391145 - 1.7034681720096305429e-1042j)  +/-  (2.08e-252, 2.08e-252j)
| (-0.33117931571527377789 - 3.1447150388469108994e-1044j)  +/-  (1.18e-253, 1.18e-253j)
| (-2.6797095161691591287 - 2.5344732983879386089e-1035j)  +/-  (1.73e-246, 1.73e-246j)
| (-5.2477244337144249688 - 8.7920432366327561712e-1033j)  +/-  (2.06e-242, 2.06e-242j)
| (-1.6641248391179069719 + 4.8126304543757314718e-1039j)  +/-  (3.98e-249, 3.98e-249j)
| (5.2477244337144249688 - 5.4171657572721585381e-1035j)  +/-  (2.25e-242, 2.25e-242j)
| (-2.0068019604802216843 + 9.3069593801475939482e-1047j)  +/-  (3.6e-248, 3.6e-248j)
| (2.3417599962877077336 + 2.7098519444367699621e-1045j)  +/-  (2.81e-247, 2.81e-247j)
| (4.4763619773108684158 + 8.0230028488022198243e-1044j)  +/-  (2.87e-243, 2.87e-243j)
| (-3.3893569169636244452 - 5.4594401222356850268e-1051j)  +/-  (5.49e-245, 5.49e-245j)
| (-1.3246623257943697578 - 2.8006656424909815359e-1056j)  +/-  (3.73e-250, 3.73e-250j)
| (3.0324042278316759091 - 6.0316128364292736714e-1049j)  +/-  (1e-245, 1e-245j)
| (0.66509007143132391145 + 7.7355610899557887668e-1058j)  +/-  (2.01e-252, 2.01e-252j)
| (0.99516242227121542187 - 3.5299988283793685722e-1056j)  +/-  (2.92e-251, 2.92e-251j)
| (3.3893569169636244452 + 3.8223153954274605054e-1054j)  +/-  (5.41e-245, 5.41e-245j)
| (-4.6549697258467558e-1078 + 8.1383022320714195585e-1077j)  +/-  (4.81e-1075, 4.81e-1075j)
| (-4.1005678299003455187 + 3.816336202637440357e-1057j)  +/-  (9.27e-244, 9.27e-244j)
| (0.33117931571527377789 + 1.6534662917939904926e-1066j)  +/-  (9.5e-254, 9.5e-254j)
-------------------------------------------------
The weights are:
| (6.4941098470080751016e-28 - 1.5428874290093815981e-948j)  +/-  (2.07e-62, 6.68e-181j)
| (4.6269971592536019603e-12 - 8.7635846907007137281e-936j)  +/-  (4.17e-51, 1.35e-169j)
| (1.7152654432944180453e-09 - 1.1191077871470782867e-934j)  +/-  (9.2e-48, 2.97e-166j)
| (6.4941098470080751016e-28 + 6.8128146509855326783e-948j)  +/-  (2.04e-63, 6.58e-182j)
| (0.018067667793631100033 + 8.9398760419128964554e-930j)  +/-  (8.9e-24, 2.87e-142j)
| (1.4648275330595902194e-36 + 3.5426459501554302891e-953j)  +/-  (2.92e-67, 9.4e-186j)
| (1.0808867671606702996e-31 + 7.8193111069988080717e-951j)  +/-  (1.47e-66, 4.75e-185j)
| (5.2466036568024398576e-22 - 9.0438511130810734049e-945j)  +/-  (3.07e-62, 9.91e-181j)
| (1.878562410500981606e-17 + 1.4120218600958698082e-940j)  +/-  (3.24e-58, 1.04e-176j)
| (9.5176435166503861426e-25 - 7.5959917314347424287e-946j)  +/-  (1.41e-62, 4.54e-181j)
| (1.4648275330595902194e-36 - 1.0384901144170695972e-953j)  +/-  (1.23e-69, 3.96e-188j)
| (1.1381543651314730052e-06 + 7.1582228346397434745e-933j)  +/-  (1.94e-47, 6.27e-166j)
| (1.6096442321556575538e-13 - 1.5643239193318249508e-936j)  +/-  (6.27e-55, 2.02e-173j)
| (1.946534713913972222e-08 + 5.0685395319697626387e-935j)  +/-  (4.41e-55, 1.42e-173j)
| (2.8286225855219478636e-14 + 2.6041232396479021711e-937j)  +/-  (7.36e-56, 2.37e-174j)
| (0.079665090822099851565 - 2.029229580167256706e-929j)  +/-  (2.65e-22, 8.54e-141j)
| (0.055380981172343974052 + 2.0365941583887610834e-929j)  +/-  (5.19e-27, 1.67e-145j)
| (1.1381543651314730052e-06 + 1.2841194297430324092e-933j)  +/-  (1.7e-52, 5.48e-171j)
| (0.0085607568720535448778 - 2.6570617393907202888e-930j)  +/-  (2.39e-39, 7.72e-158j)
| (1.946534713913972222e-08 + 4.784756266890730909e-934j)  +/-  (1.56e-51, 5.02e-170j)
| (1.3608699530411253459e-19 - 2.9815066916149206833e-942j)  +/-  (4.98e-61, 1.61e-179j)
| (0.0014372328298033886494 - 5.0373887680520663027e-931j)  +/-  (5.02e-45, 1.62e-163j)
| (0.0001283088252310737838 - 6.8447875929231627905e-932j)  +/-  (7.58e-49, 2.44e-167j)
| (1.4036412905402351232e-15 - 6.8013816564053277245e-939j)  +/-  (6.51e-58, 2.1e-176j)
| (1.4036412905402351232e-15 + 4.9137914389723780786e-940j)  +/-  (3.09e-64, 9.97e-183j)
| (1.6096442321556575538e-13 + 4.3957322703860541603e-938j)  +/-  (1.39e-62, 4.5e-181j)
| (1.0808867671606702996e-31 - 3.0284492268627684195e-950j)  +/-  (9.12e-70, 2.94e-188j)
| (5.2466036568024398576e-22 + 5.466250380698564822e-944j)  +/-  (7.69e-64, 2.48e-182j)
| (3.2738712768286969964e-05 + 7.9586545092799115083e-932j)  +/-  (1.73e-52, 5.58e-171j)
| (9.5176435166503861426e-25 + 1.4879308675073001318e-946j)  +/-  (5.51e-70, 1.78e-188j)
| (4.6269971592536019603e-12 - 1.8104588316220230143e-937j)  +/-  (5.87e-63, 1.89e-181j)
| (0.0001283088252310737838 - 2.2631474565327744967e-931j)  +/-  (7.77e-53, 2.5e-171j)
| (0.0038020039638061130392 + 2.7696526460498904504e-930j)  +/-  (8.77e-50, 2.83e-168j)
| (1.878562410500981606e-17 - 1.4630030169440523117e-941j)  +/-  (7.17e-67, 2.31e-185j)
| (1.3608699530411253459e-19 + 4.0177919174624678542e-943j)  +/-  (3.87e-68, 1.25e-186j)
| (1.0552387660453771377e-10 + 1.1237119997864174996e-936j)  +/-  (3.01e-63, 9.71e-182j)
| (1.0552387660453771377e-10 + 3.2798971904905826951e-935j)  +/-  (4.08e-61, 1.31e-179j)
| (0.034331038905204970247 - 1.3852749793515547189e-929j)  +/-  (7.27e-50, 2.34e-168j)
| (6.7916208668100064072e-06 - 5.3922347336964014902e-933j)  +/-  (7.08e-60, 2.28e-178j)
| (1.7152654432944180453e-09 - 7.8231927958303678374e-936j)  +/-  (8.68e-63, 2.8e-181j)
| (2.8286225855219478636e-14 - 1.1556826335147026219e-938j)  +/-  (2.37e-65, 7.65e-184j)
| (0.10649991347469592623 + 2.6348126580893125768e-929j)  +/-  (2.34e-51, 7.54e-170j)
| (0.12582552851831580602 - 3.1425722495782355258e-929j)  +/-  (1.55e-51, 4.98e-170j)
| (0.0038020039638061130392 + 1.2339374941089641361e-930j)  +/-  (2.23e-57, 7.18e-176j)
| (1.6321353086929720171e-07 - 2.7703179388284187885e-934j)  +/-  (1.39e-61, 4.49e-180j)
| (0.034331038905204970247 - 8.5227020147246239423e-930j)  +/-  (1.32e-55, 4.24e-174j)
| (1.6321353086929720171e-07 - 1.9497340835041566652e-933j)  +/-  (1.47e-62, 4.75e-181j)
| (0.018067667793631100033 + 4.9498796963588864784e-930j)  +/-  (3.2e-57, 1.03e-175j)
| (0.0085607568720535448778 - 5.3366143350628244181e-930j)  +/-  (4.36e-58, 1.41e-176j)
| (6.7916208668100064072e-06 - 2.4628369426695845819e-932j)  +/-  (9.51e-62, 3.07e-180j)
| (0.00045267670037102584171 + 1.9351719387090279811e-931j)  +/-  (3.78e-60, 1.21e-178j)
| (0.055380981172343974052 + 1.387353514869100321e-929j)  +/-  (1.53e-57, 4.81e-176j)
| (0.0014372328298033886494 - 1.2764793332603619555e-930j)  +/-  (2.68e-60, 8.6e-179j)
| (0.10649991347469592623 + 3.1892887169959607521e-929j)  +/-  (4.13e-58, 1.29e-176j)
| (0.079665090822099851565 - 2.7034003480784266084e-929j)  +/-  (3.79e-58, 1.19e-176j)
| (0.00045267670037102584171 + 5.5824859346105912677e-931j)  +/-  (6.2e-61, 2.02e-179j)
| (0.13161589425991599701 + 3.4547160522785492783e-929j)  +/-  (2.4e-58, 7.56e-177j)
| (3.2738712768286969964e-05 + 2.0713341544479501104e-932j)  +/-  (4.76e-62, 1.55e-180j)
| (0.12582552851831580602 - 3.4553560165669104797e-929j)  +/-  (1.38e-58, 4.14e-177j)
